# Integer factoring again

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Are there any algorithms which factor integers purely algebraically - no trial and error, no guessing, no probability?

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Anyone interested in writing one?

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You can't just "write" a fast algorithm that factors an integer...that's why it's been an open problem for so long.

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there is no algorithm to do this robustly if you find one, I'm sure many number theoriests would be happy to hear it. there is one trick you should look at numbers that are less then the square root, it is impossible for prime factors of an integer to be greater then the square root of itunless it itself is prime

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Quote:
 Original post by dtrainorAre there any algorithms which factor integers purely algebraically - no trial and error, no guessing, no probability?
Quote:
 Original post by eleusiveYou can't just "write" a fast algorithm that factors an integer...that's why it's been an open problem for so long.
Quote:
 Original post by timwthere is no algorithm to do this robustly if you find one, I'm sure many number theoriests would be happy to hear it.
Observe that there is nothing in my original post which talks about speed - only about being algebraically deterministic. Writing an algorithm does not alter the intrinsic characteristics of the problem, it only helps to expose them.

[Edited by - dtrainor on July 27, 2005 8:20:26 AM]

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Quote:
 Original post by dtrainorObserve that there is nothing in my original post which talks about speed - only about being algebraically deterministic.

Define "algebraically deterministic".

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Quote:
 Original post by alvaroDefine "algebraically deterministic".
In this case: Set up and solve a well defined system of equations. At the end of that process either: no solution exists, in which case the number is prime. You obtain a solution, in which case it is a non-trivial factor of a composite number. At no time do you ever "test" a value to see if works or to find the remainder.

[Edited by - dtrainor on July 27, 2005 4:14:11 PM]

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Try to factor using algebra?? What would be your unknown or X and Y? Anyways, what kind of equation can you get that doesn't turn up null or in other words 0=0??

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Take a look at this: http://en.wikipedia.org/wiki/General_Number_Field_Sieve

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